Half-Life 2 Walkthrough -> A Great Day
We proceed to Dr. Kleiner's lab. There, he'll say he's finished his teleport and will immediately send you and Alex to his old friend Eli's lab (Black Mesa East):
The Good Old Suit
Here, Barney will offer you the chance to change into the good old suit. When the door leading to the suit opens, a "Headcrab" named Lamar, tamed by Dr. Kleiner, will appear (jumping down from above). (By the way, Barney, even though Lamar's stinger has been removed, is terrified of him.)
Proceed to the room with the teleporter, which Kleiner will open using the panel behind the photo of scientists from the old Black Mesa. Contact Alyx's father, Dr. Eli. Alyx goes through the teleporter. Stand at the panel to the right of the teleporter, where three cables are plugged in. When one of them falls off, plug it back in.
The teleporter starts glitching, sending us to various locations—Brin's office in the Citadel, the desert, the sea, the lab—and eventually we find ourselves outside the window of Kleiner's lab. The doctor tells us to run. We climb down from the balcony and run.
We head to the railroad. When we get down to the train cars, we'll come under fire from two cops on the right. Ignoring them, we run in the other direction. There's an open train car there. We grab a crate from it and carry it out onto the platform.